Transient and steady state results for two parallel queues

This paper lists numerical results for a system with two parallel queues in which arriving customers always join the shorter queue. These results enable us to discuss how fast the expected queue length converges toward its equilibrium, provided the arrivals are below the capacity of the service facility. It also shows how fast the expected queue length increases in case the traffic flow is at or above the capacity of the service facility. Finally, it is shown that the system under consideration behaves very similar to a two-server queue.     

基于系统柔性的MTS-MTO混合生产决策

研究生产商采用MTS、MTO混合作业的方式为不同客户提供产品和服务的策略。计划利用一组可灵活控制的动态设备处理那些不同需求的MTS和MTO生产业务,为此,我们开发了一个多服务台的排队模型,利用拟生灭过程和相位型分布得到了MTS、MTO排队系统平衡条件和稳态概率矩阵几何解。通过求解分块矩阵方程组,给出了系统队列长度、平均等待队长、顾客服务水平等绩效测度指标。建立了系统运作成本最优化的数学模型,采用搜索算法,确定了关键参数的边界值,找到了混合系统运作的最优策略。数值模拟和系统绩效比较分析结果显示：（1）动态切换策略能够更快速的帮助MTS恢复目标库存量,控制系统缺货风险,降低库存持有成本;（2）找到了满足顾客服务水平的最少的设备配置数量和库存成本最低的生产切换时间,且动态系统的平均队列长度低于静态系统;（3）混合运作策略减少了约2/3的静态系统平均队列长度,企业在队列长度减小的窗口期内可以接受更多订单和缩短MTO订单交货时间。     

Service and Price Competition When Customers Are Naive

We consider a system of two service providers each with a separate queue. Customers choose one queue to join upon arrival and can switch between queues in real time before entering service to maximize their spot utility, which is a function of price and queue length. We characterize the steady‐state distribution for queue lengths, and then investigate a two‐stage game in which the two service providers first simultaneously select service rates and then simultaneously charge prices. Our results indicate that neither service provider will have both a faster service and a lower price than its competitor. When price plays a less significant role in customers’ service selection relative to queue length or when the two service providers incur comparable costs for building capacities, they will not engage in price competition. When price plays a significant role and the capacity costs at the service providers sufficiently differ, they will adopt substitutable competition instruments: the lower cost service provider will build a faster service and the higher cost service provider will charge a lower price. Comparing our results to those in the existing literature, we find that the service providers invest in lower service rates, engage in less intense price competition, and earn higher profits, while customers wait in line longer when they are unable to infer service rates and are naive in service selection than when they can infer service rates to make sophisticated choices. The customers’ jockeying behavior further lowers the service providers’ capacity investment and lengthens the customers’ duration of stay.     

Judicious order acceptance and order release in make-to-order manufacturing systems

This paper explores a two-stage input control system for fixed capacity make-to-order manufacturing systems (with heavy job tardiness penalties), that selectively accepts incoming orders and holds the accepted ones in a pre-shop queue prior to releasing them to the shop floor. Single-stage input control systems that only allow orders to be delayed in a pre-shop queue (i.e. they do not allow some orders to be rejected) have been previously investigated and found to negatively impact overall due-date performance. The hypothesis motivating this research is that judiciously rejecting a subset of incoming orders can prevent the order release queue from being overloaded when a surge of demand occurs. The input control system is evaluated via experiments using a discrete-event simulation model of a fixed capacity manufacturing system. The experiments reported here suggest that holding orders in the pre-shop queue does not improve due date performance, and that judiciously rejecting orders on its own is a viable alternative mechanism of input control that can deliver improved performance.     

Optimal Allocation of Effort to Software Maintenance: A Queuing Theory Approach

We develop variations of the M|G|1 queue to model the process of software maintenance within organizations and use these models to compute the optimal allocation of resources to software maintenance. User requests are assumed to arrive following a Poisson process and a binomial distribution is used to model duplication of requests. We obtain expressions for expected queue lengths with an exponential server using an N‐policy for an integer N≥1. We also obtain the optimal batching size and mean service rate by minimizing the total cost consisting of the cost of the server, the cost of waiting, and the fixed cost of maintenance, if applicable.     

USING RUN-LENGTH DISTRIBUTIONS OF CONTROL CHARTS TO DETECT FALSE ALARMS

Run-length distributions for various statistical process-control charts and techniques for computing them recently have been reported in the literature. The real advantages of knowing the run-length distribution for a process-control chart versus knowing only the associated average-run length of the chart have not been exploited. Our purpose is to use knowledge of the run-length distribution as an aid in deciding if an out-of-control signal is a true signal or merely a false alarm. The ability to distinguish between true and false signals is important, especially in operations where it is costly to investigate the causes of out-of-control conditions. Knowledge of the run-length distribution allows us to compute likelihood ratios, which are simple to calculate and to interpret and which are used to determine the odds of obtaining an out-of-control signal at a particular run length when a shift in the process mean actually has occurred vis-a-vis no such shift. We extend our analysis in a Bayesian sense by incorporating prior information on the distribution of the shift size of the process mean, combined with the likelihood ratio obtained from the run-length distribution, to determine if a shift larger than a critical size has occurred. We give examples for the Shewhart chart, the exponentially weighted moving-average chart, and the special-cause control chart for processes with autocorrelated observations. The examples show that the current recommended usage of the average-run length alone as a guide for determining whether a signal is a false alarm or otherwise can be misleading. We also show that the performance of the traditional charts, in terms of their average-run length, can be enhanced in many instances by using the likelihood-ratio procedure.     

Sectoral Queuing in a Transitional Economy: The Case of Nicaragua in the 1990s

Abstract. Using microdata from the 1993 and 1998 Living Standards Measurement Survey (LSMS) of Nicaragua, this paper analyzes the propensity of informal sector workers to queue for formal sector employment as well as employer behavior related to the selection of individuals from the informal sector queue. The nature of the queue is also examined over time to determine informal sector workers’ response to national market‐based reforms. The results indicate that informal workers do indeed queue for formal sector employment and the nature of the queue has become more pronounced during the time period under consideration.     

SHIFTING PRODUCTION BOTTLENECKS: CAUSES,CURES, AND CONUNDRUMS

We examine the phenomenon of shifting production bottlenecks from an analytic perspective. We quantify the propensity of a work center to be a bottleneck, defined as maximal queue length, using a simple Jackson production network model. Comparison of the analytic model against an empirical simulation-based model shows that the two are in good agreement. A scalar measure of bottleneck shiftiness is proposed and used to investigate several policies for mitigating shiftiness. Simulation experiments show that several commonly observed managerial policies for coping with shifting bottlenecks actually increase shiftiness, but that shiftiness declines when the capacity of nonbottleneck resources is increased.     

Health economic modeling to support surgery management at a Swedish hospital

Elective surgery management typically deals with a queue of patients that have to be scheduled for surgery within a certain time frame, considering both medical and economic constraints. In order to prevent the patient queue and waiting times from growing, surgery management has to decide whether to temporarily increase patient throughput at the regional hospital or have some patients scheduled for surgery at another hospital. In Sweden, a newly passed law states that patients who decide to receive surgery should not have to wait more than 90 days before this surgery is carried out. Therefore, if a patient decides to apply the new law by requesting surgery within 90 days, the regional hospital is obliged to arrange and pay for either in-house surgery or surgery at another hospital. In this paper, we suggest an approach using simulation including optimization for modeling surgery management decisions. We study a case based on data from a General Surgery Department at a Swedish hospital and present our results as a health economic evaluation. The results indicate an increase in the mean waiting times for medium prioritized patients when the new law is applied.     

APPROXIMATE QUEUEING NETWORK MODELS FOR CLOSED FABRICATION/ASSEMBLY SYSTEMS. PART I: SINGLE LEVEL SYSTEMS

We address the issue of performance analysis of fabrication/assembly (F/A) systems, which are systems that first fabricate components and then join the components and subassemblies into a product. Here we consider an F/A system consisting of a single assembly station with input from K fabrication stations. We assume that the system uses a Kanban control mechanism with a fixed number of kanbans circulating between each input station and the assembly station. Even with Markovian assumptions, computing an exact solution for the performance evaluation of such systems becomes intractable due to an explosion in the state-space. We develop computationally efficient algorithms to approximate the throughput and mean queue lengths. The accuracy of the approximations is studied by comparison to exact results (K = 2) and to simulations (K > 2). Part II of this paper demonstrates how these models can be used as building blocks to evaluate more complex F/A systems with multiple levels of assembly stations.     

基于顾客公平偏好的服务机制与定价研究

由于顾客异质性（单位时间等待成本不同），服务提供商通常对顾客采取分类服务策略，然而分类服务会引起服务系统中不同类型顾客之间等待时间和服务价值的差异性，从而给顾客带来心理上的不公平感，进而引起顾客在服务系统中的流动和转移，进一步影响企业收益和社会福利。本文针对非抢占M/M/1服务系统顾客分类情形为背景，由两种顾客之间期望等待时间的不同和公平偏好参数相结合构建普通顾客的公平心理效用模型，以垄断型服务系统为背景，分别从企业收益、社会福利与顾客效用三个视角进行分析。研究表明，服务提供商应对顾客采取可观测型的分类服务机制来获得最大收益；从社会福利视角，服务提供商应对顾客采取不可观测型的分类服务机制；从顾客效用视角，服务提供商应取消顾客分类服务，仅保留普通顾客。最后同现有结论进行比较分析，并进行拓展研究。本文研究对服务提供商采取合理的服务机制及相应的服务定价具有重要参考价值和指导意义。     

PERFORMANCE ANALYSIS OF AN ASSEMBLY STATION WITH INPUT FROM MULTIPLE FABRICATION LINES

We develop analytical models for performance evaluation of Fabrication/Assembly (F/A) systems. We consider an F/A system that consists of an assembly station with input from K fabrication lines. Each fabrication line consists of one or more fabrication stations. The system is closed with a fixed number of items circulating between each fabrication line and the assembly station. We present algorithms to estimate the throughput and mean queue lengths of such systems with exponential processing times. We then extend our approach to analyze F/A systems with general processing time distributions. Numerical comparisons with simulations demonstrate the accuracy of our approach.     

基于瓶颈负荷的BTO供应链响应时间优化

供应商生产的低效率是BTO供应链实际运作过程中的瓶颈,主要表现为供应链整体响应时间长和在制品库存高.针对该类供应链的瓶颈特点,利用排队模型建立了一种基于瓶颈负荷的BTO供应链响应时间优化策略.然后,通过算例分析了订单数量、等待订单数量和产能利用率,以及系统内的概率分布等参数对在制品库存水平和供应链整体响应时间的影响.最后,得出的结论表明,基于瓶颈负荷的控制对缩短供应链整体响应时间和在制品库存水平的控制均是有效的.     

随机动态装卸混合问题的分区求解策略

针对需求服从一般分布的随机动态装卸混合问题,提出一种求解该问题的分区求解策略,分析了需求稀少和需求密集情况下该策略的渐近性.仿真比较了需求服从一般分布情形下分区求解策略、随机队列中位策略、多车场随机队列中位策略和堆栈策略的求解效果,以及需求服从一般分布和需求服从均匀分布情形下分区求解策略的求解效果.结果表明,对于需求服从一般分布的随机动态装卸混合问题,分区求解策略是一种有效的求解策略.     

A Behavioral Training Program for Managers in City Government

A management training program based on Organizational Behavior Management (OBM) principles was conducted for 32 first-level and upper-level managers in city government. Managers then conducted 19 different behavior change projects with their employees. Each project is described in terms of the number of subjects, dependent and independent variables, length, research design, reliability measures, and results. The overall program was evaluated in terms of behavior change, traineelmanager satisfaction with the training, and effectiveness. Twenty-nine change ratios were calculated by comparing the intervention performance mean with the baseline mean, and in all cases, the change ratio showed that productivity improved. In fourteen case's, productivity at least doubled. The results indicate that employee performance in a governmental organization can be enhanced significantly by use of OBM principles.     

A REVIEW OF THE KANBAN PRODUCTION CONTROL RESEARCH LITERATURE

Station interdependence, blocking caused by finite buffer capacities, and periodic material handling make modeling and analysis of kanban-controlled lines challenging. Also, one must consider flows of material as well as flows of kanbans. The many models given in the literature contribute to the confusion and debate that often characterize kanban research. The only element common to all kanban systems appears to be finite buffer capacities. I describe blocking by total queue size, blocking by part type, and the single-card and twocard systems. I review the kanban literature and organize it by type of system and decision area. First, I discuss elements of system design, including setting kanban numbers, performance measures, material-handling frequencies, and container sizes. Then I cover the production control topics of sequencing and batch-sizing. I conclude with a comparison of kanban and conventional methods of production control and with suggestions for future research.     

OPTIMAL RENEGING DECISIONS IN A G/M/1 QUEUE

This paper is an analysis of the optimal reneging decision of a customer who joins a G/M/1 queue, having imperfect information about the queue. It is assumed that a customer receives a constant, known reward upon completion of service and incurs a cost proportional to the time spent in the queueing system. It is also assumed that a customer revises his estimated remaining waiting time in the system based on his initial estimate and observations of service time. Thus, a customer will renege when his estimated cost of remaining in the system exceeds his reward. The probability of a customer reneging during any given service is determined. Finally, it is shown how this probability varies with the parameters of the customer.     

Call Center Delay Announcement Using a Newsvendor‐Like Performance Criterion

The problem of estimating delays experienced by customers with different priorities, and the determination of the appropriate delay announcement to these customers, in a multi‐class call center with time varying parameters, abandonments, and retrials is considered. The system is approximately modeled as an M(t)/M/s(t) queue with priorities, thus ignoring some of the real features like abandonments and retrials. Two delay estimators are proposed and tested in a series of simulation experiments. Making use of actual state‐dependent waiting time data from this call center, the delay announcements from the estimated delay distributions that minimize a newsvendor‐like cost function are considered. The performance of these announcements is also compared to announcing the mean delay. We find that an Erlang distribution‐based estimator performs well for a range of different under‐announcement penalty to over‐announcement penalty ratios.     

Optimal Choice for Appointment Scheduling Window under Patient No‐Show Behavior

Observing that patients with longer appointment delays tend to have higher no‐show rates, many providers place a limit on how far into the future that an appointment can be scheduled. This article studies how the choice of appointment scheduling window affects a provider's operational efficiency. We use a single server queue to model the registered appointments in a provider's work schedule, and the capacity of the queue serves as a proxy of the size of the appointment window. The provider chooses a common appointment window for all patients to maximize her long‐run average net reward, which depends on the rewards collected from patients served and the “penalty” paid for those who cannot be scheduled. Using a stylized M/M/1/K queueing model, we provide an analytical characterization for the optimal appointment queue capacity K, and study how it should be adjusted in response to changes in other model parameters. In particular, we find that simply increasing appointment window could be counterproductive when patients become more likely to show up. Patient sensitivity to incremental delays, rather than the magnitudes of no‐show probabilities, plays a more important role in determining the optimal appointment window. Via extensive numerical experiments, we confirm that our analytical results obtained under the M/M/1/K model continue to hold in more realistic settings. Our numerical study also reveals substantial efficiency gains resulted from adopting an optimal appointment scheduling window when the provider has no other operational levers available to deal with patient no‐shows. However, when the provider can adjust panel size and overbooking level, limiting the appointment window serves more as a substitute strategy, rather than a complement.     

小波包与混沌集成的股票市场预测新方法

基于小波包变换和混沌理论提出了一种股票市场建模及其预测的新方法,既能刻划时间序列的规律,又能捕捉混沌状态的特征.首先,应用小波包变换对上证综指和深证成指日收益率序列进行三层分解,分别得到第三层从低频到高频八个频率成分的时序,并在此基础上作进一步分析,结果表明中国股市存在混沌特性;然后,应用混沌理论分别建立从低频到高频八个时序的预测模型,分别对八个时序进行预测;最后,基于小波包理论对混沌模型预测的结果予以重构,实现对原始收益率序列的预测.与现有方法比较,结果表明该方法具有较高的精度,有极大的应用范围.